Just for the fun of it, and in the name of science, I tried a variation of your theory on cutting a kerf on one side to move a small tree towards the needed lean.
I had to cut a small pine on a steep bank that grew out of the ground at about a 30 degree angle for about 3 feet, then made an abrupt turn nearly straight up and just slightly up the hill.
The sharply angled lower 3 feet leaned down the hill. This put the hinge wood close to the ground above the center of mass, so that if cut close to the ground the favor was down the hill. If cut at the crook the favor was slightly up the hill.
I wanted the tree to go up the hill, so I cut into it above the crook until it started to open the kerf on the back cut with no face. This moved the top of the tree farther up hill. Then I faced and back cut the stump, and it tried to set back. So I moved back to the upper cut and cut a little deeper, the top moved some more, but not enough.
I wound up cutting the top cut until it peeled off and then cut the stump off.
I would have been better off to have cut a small face in the upper part and let it close on the face, or make a more open face and just cut if off.
In relevance to your situation I could not get the top to move very far before it wanted to split and fall without a face.
On the plumb bob, I don't carry a weight and string, but use my ax often. It is not nearly as precise, but it gives a good reference.
When there is absolutely nothing level or square in sight and the whole world seems to be turned on edge, I need a good reference to judge the lean.
With an ax you have to be careful not to influence it with your grip. You have to pinch the handle so that the head hangs down with out being pulled off to one side or the other. You also cannot see the whole tree at one time. I will often line up where my hinge is going to be, then site up one side of the handle then the other.
Bushler is absolutely correct, you have to judge the whole mass of the tree, not just the trunk.
A while back some one on here commented on The wind blowing the plumb bob over and making it ineffective. If the wind is fairly steady and from generally the same direction, it can make directional falling a "breeze".